studying

The function f is given by f(x) = 1000^x. If f(x) = 10, what is the value of x? a. 1/3 b. 1/2 c. 3 d. 3√1000

a. 1/3

The graphs show the residual plots resulting from cubic, quadratic, and linear regressions calculated on the same data set. Based on the plots, which of the following statements is best supported by the results? a. The cubic model should be used. b. The quadratic model should be used. c. The linear model should be used. d. A different regression should be calculated because none of the given three regressions is appropriate.

a. The cubic model should be used.

x | 3 | 5 | 7 | ------------------ y | 85 | 95 | 105 | The table gives values of an arithemetic sequence An for selected values of n. Which if the following linear functions is constructed from the initial value of A0 (with n=0) and common difference of the sequence? a. f(x) = 70 + 5x b. f(x) = 70 + 10x c. f(x) = 75 + 5x d. f(x) = 75 + 10x

a. f(x) = 70 + 5x

The function h is given by h(x) - a - b^-x, where a < 0 and b > 1. Which of the following describes h and its graph in the xy-plane? a. h is increasing, and the graph of h is concave down. b. h is increasing, and the graph of h is concave up. c. h is decreasing, and the graph of h is concave down. d. h is decreasing, and the graph of h is concave up.

a. h is increasing, and the graph of h is concave down.

A drop of water hits the surface of a lake and forms concentric circular ripples. The radius, in inches, of the circle enclosed by the outer ripple increases as a function of time t, in minutes, and is modeled by the function r given by r (t) = 25\2t + I. Which of the following gives the area of the circle enclosed by the outer ripple, in square inches, as a function of time t, in minutes? (Note; The area of a circle with radius x is given by A = (pi)(x)^2.) a. 50(pi)(t) + 25(pi) b. 1250(pi)(t) + 625(pi) c. 25√2(pi)(t)^2 + 1 d. 25(pi)(t)^2√2(t) + 1

b. 1250(pi)(t) + 625(pi)

year | 2004 | 2008 | 2012 | 2016 | ----------------------------------- Pop. | 22.4 | 24.3 | 26.0 | 27.9 | (mil.) The table gives the pop., in millions, of a certain region for selected years. An exponential regression of the form f(x) = a x b^x is calculated for the five data points, where x = 4 represents 2004 and x = 8 represents 2008. Based on using the model f to predict the future pop., in what year will the pop. first reach 35 million? a. 2025 b. 2030 c. 2033 d. 2037

b. 2030

The function g is given by g(x) = 4 x 2^(3 + x). The function g can also be expressed as which of the following? a. 32 + 2^x b. 32 x 2^x c. 32 + 8^x d. 512 x 8^x

b. 32 x 2^x

The first term of a geometric sequence is 2/3. The next three terms are 1/2, 3/8, and 9/32. What is the tenth term of the sequence? a. 19,683/524,288 b. 6,561/131,072 c. 524,288/59,049 d. 2,097,152/177,147

b. 6,561/131,072

x | 1 | 2 | 3 | 4 | 5 y | 20 | 30 | 40 | 70 | 100 The table gives five coordinate pairs (x, y). The function y = f(x) is a model based on a linear regression of the five pairs. The function y = 9(a) is a model based on an exponential regression y = ab of the five pairs. Because of the limited number of data points for the residual plots, it is difficult to determine if the residuals show a pattern. As a result, both models f and g are being considered. The value k represents the sum of the absolute values of the errors (residuals) of the linear model f. The value p represents the sum of the absolute values of the errors (residuals) of the exponential model g. If the selection of an appropriate model is based on the errors (residuals), which of the following is true? a. Because k>p, the linear model is preferred. b. Because k>p, the exponential model is preferred. c. Because k<p, the linear model is preferr

b. Because k>p, the exponential model is preferred.

The graph of the function y = f(x) is given. Which of the following is the graph of y = f -1(x)? a. graph one (decreasing) b. graph two (increasing) c. graph three (decreasing) d. graph four (increasing)

b. graph two (increasing)

The function f is given by f(x) = k + a x b^x, where a < 0, b > 1, and k is a real number. Which of the following is true? a. lim x -> -∞ f(x) = -k b. lim x -> -∞ f(x) = k c. lim x -> ∞ f(x) = -k d. lim x -> ∞ f(x) = k

b. lim x -> -∞ f(x) = k

In the xy-plane, the graphs of the linear function L and the exponential function E both pass through the points (0,2) and (1,6). The function f is given by f(x) = L(x) — E(x). What is the maximum value of f? a. 0.007 b. 0.172 c. 0.540 d. 1.002

c. 0.540

A certain hobby shop wants to attract customers on slow sales days by offering a new discount. The shop offers a 1.5% discount on Wednesdays with an added bonus for repeat customers. For customers who make purchases on successive Wednesdays, their discount is doubled from the previous Wednesday. For example, a certain customer makes purchases on three successive Wednesdays and receives 1.5% (week 1), 3% (week 2), and 6% (week 3) discounts on those three Wednesdays. Based on this pattern, what is the first successive week that a customer's discount would exceed the purchase price of an item? a. 6 b. 7 c. 8 d. 11

c. 8

x | 4 | 5 | 6 | 7 | 8 | --------------------------- y | 2 | 3 | 4 | 5.5 | 7 | Linear | y = 1.25x - 3.2 Quadratic | y = 0.107x^2 - 0.036x + 0.443 Exponential | y = 0.606(1.365)^x The fust table gives selected coordinate pairs (x, 1) that are a part of a larger data set. Using the five data points, three regressions were calculated, and the resulting linear, quadratic, and exponential equations are provided in the second table. It is known that the resulting linear, quadratic, and exponential regressions fit these five data points well. Which of the following additional pieces of information could help select'a single best model? a. Knowing that as the x-values increase, the y-values increase without bound. b. Knowing that the minimum y-value in the data set is less than 1. c. Knowing that when the x-values are negative, the corresponding y-values are always between 0 and 1. d. Knowing that the y in

c. Knowing that when the x-values are negative, the corresponding y-values are always between 0 and 1.

Terms in a sequence are given by Sn = 4n + 7, for n =0,1,2,3,....Which of the following describes the sequence? a. The sequence is geometric with an initial value of 7 and a common ratio of 4. b. The sequence is geometric with an initial value of 11 and a common ratio of 4. c. The sequence is arithmetic with an initial value of 7 and a common difference of 4. d. The sequence is arithmetic with an initial value of 11 and a common difference of 4.

c. The sequence is arithmetic with an initial value of 7 and a common difference of 4.

x | -1 | 0 | 1 | 2 | ---------------------- f(x) | 1 | 4 | 5 | -1 | x | -1 | 1 | 4 | 10 | ----------------------- g(x)| 0 | 1 | 2 | -1 | The tables give values of the functions f and g for selected values of x. What is the value of g -1 (f(2))? a. -1 b. 0 c. 4 d. 10

d. 10

The number of bacteria in a dish is 1150 at time t = 0 hours. The number of bacteria in the dish doubles every 3 hours. If the function B gives the number of bacteria in the dish at time t hours t ≥ 0, which of the following could define B(t)? a. 1150 x (3√2)^(t/3) b. 1150 x 2^t c. 1150 x (2^3)^t d. 1150 x 2^(t/3)

d. 1150 x 2^(t/3)

The graphs of y = f(x) and y = g(x) are given.What is the value of f(f(g(1)))? a. -2 b. 0 c. 3 d. 4

d. 4

The function f is given by f(x) = x + 2 if f -1 (n) = 4, what is the value of n? a. -4 b. 1/4 c. 2 d. 6

d. 6

The fourth term of a geometric sequence is 7, the fifth term is 28/3, and the kth term is 7168/243. The solution to which of the following equations gives the value of k? a. 4(3/4)^(x-7) = 7168/243 b. 7(3/4)^(x-4) = 7168/243 c. 4(4/3)^(x-7) = 7168/243 d. 7(4/3)^(x-4) = 7168/243

d. 7(4/3)^(x-4) = 7168/243

A ball is dropped from a height of 10 feet. The ball repeatedly bounces, and the maximum height of the ball after each bounce is 20% less than the previous maximum height. Which of the following arguments is correct regarding a sequence that can be used to model the successive maximum heights, in feet? a. An arithmetic sequence is appropriate because each successive height would be found by subtracting 2 from the previous height. b. An arithmetic sequence is appropriate because each successive height would be found by multiplying the previous height by 0.8. c. A geometric sequence is appropriate because each successive height would be found by subtracting 2 from the previous height. d. A geometric sequence is appropriate because each successive height would be found by multiplying the previous height by 0.8.

d. A geometric sequence is appropriate because each successive height would be found by multiplying the previous height by 0.8.

The first term in a geometric sequence is g1 = 5. For n ≥ 2, the terms of the geometric sequence are given by gn = 3 x g(n-1). For which of the following functions is gn = f(n) for positive integer values of n? a. f(x) = 3 x 5^n b. f(x) = 3 x 5^(n-1) c. f(x) = 5 x 3^n d. f(x) = 5 x 3^(n-1)

d. f(x) = 5 x 3^(n-1)

The graph of the function f is given. If g is the function given by g(x) = 2x, which of the following is the graph of the composite function y = f(g(x)) ? a. graph one b. graph two c. graph three d. graph four

d. graph four